Antedependence models for longitudinal data

Antedependence Models for Longitudinal Data

Volumn , Issue , 2009, Pages 1-271

  Zimmerman, Dale L ^a   Núñez Antón, Vicente A ^b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85056389020     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420064278     Document Type: Book

References (126)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
2. Albert, J. M. (1992). A corrected likelihood ratio statistic for the multivariate regression model with antedependent errors. Communications in Statistics – Theory and Methods, 21(7), 1823–1843.
3. Albuquerque, L. G. and Meyer, K. (2005). Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations. Livestock Production Science, 93, 213– 222.
4. Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. New York: John Wiley & Sons, Inc.
5. Azzalini, A. (1994). Logistic regression for autocorrelated data with application to repeated measures. Biometrika, 81(4), 767–775.
6. Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004). Hierarchical Modeling and Analysis for Spatial Data. Boca Raton, Florida: Chapman & Hall/CRC.
7. Barrett, W. W. and Feinsilver, P. J. (1978). Gaussian families and a theorem on patterned matrices. Journal of Applied Probability, 15(3), 514–522.
8. Belcher, J., Hampton, J. S., and Tunnicliffe Wilson, G. (1994). Parameterization of continuous time autoregressive models for irregularly sampled time series data. Journal of the Royal Statistical Society, Series B, 56(1), 141– 155.
9. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with Discussion). Journal of the Royal Statistical Society, Series B, 36(2), 192–236.
10. Besag, J. and Kooperberg, C. (1995). On conditional and intrinsic autoregression. Biometrika, 82(4), 733–746.
11. Bickel, P. and Levina, E. (2008). Regularized estimation of large covariance matrices. Annals of Statistics, 36(1), 199–227.
12. Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. San Francisco: Holden Day.
13. Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd ed. New York: Springer-Verlag.
14. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference, 2nd ed. New York: Springer-Verlag.
15. Byrne, P. J. (1996). Multivariate analysis with an autoregressive covariance model. Communications in Statistics – Theory and Methods, 25(3), 555– 569.
16. Byrne, P. J. and Arnold, S. F. (1983). Inference about multivariate means for a nonstationary autoregressive model. Journal of the American Statistical Association, 78(384), 850–855.
17. Carlin, B. P. and Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC Press.
18. Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd ed. Belmont, CA: Duxbury Press.
19. Cepeda, E. C. and Gamerman, D. (2004). Bayesian modeling of joint regression for the mean and covariance matrix. Biometrical Journal, 46(4), 430– 440.
20. Cepeda-Cuervo, E. and Núñez-Antón, V. (2007). Bayesian joint modelling of the mean and covariance structures for normal longitudinal data. SORT, 31(2), 181–200.
21. Cepeda-Cuervo, E. and Núñez-Antón, V. (2009). Bayesian modelling of the mean and covariance matrix in normal nonlinear models. Journal of Statistical Computation and Simulation, 79(6), 837–853.
22. Chen, R. and Tsay, R. S. (1993). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88(421), 298–308.
23. Cox, D. R. and Snell, E. J. (1989). Analysis of Binary Data, 2nd ed. London: Chapman and Hall/CRC Press.
24. Cressie, N. (1993). Statistics for Spatial Data. New York: John Wiley & Sons, Inc.
25. Crowder, M. J. and Hand, D. J. (1990). Analysis of Repeated Measures. London: Chapman & Hall.
26. de Boor, C. (2001). A Practical Guide to Splines (Revised ed.), New York: Springer.
27. Daniels, M. J. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika, 89(3), 553– 566.
28. Davis, C. S. (2002). Statistical Methods for the Analysis of Repeated Measurements. New York: Springer-Verlag.
29. Davison, A. C. and Sardy, S. (2000). The partial scatterplot matrix. Journal of Computational and Graphical Statistics, 9(4), 750–758.
30. Dawson, K. S., Gennings, C., and Carter, W. H. (1997). Two graphical techniques useful in detecting correlation structure in repeated measures data. The American Statistician, 51(3): 275–283.
31. Dempster, A. P. (1972). Covariance selection. Biometrics, 28(1), 157–175.
32. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with Discussion). Journal of the Royal Statistical Society, Series B, 39(1), 1–38.
33. Diggle, P. J. (1988). An approach to the analysis of repeated measurements. Biometrics, 44(4), 959–971.
34. Diggle, P. J., Heagerty, P. J., Liang, K. Y., and Zeger, S. L. (2002), Analysis of Longitudinal Data, 2nd ed. New York: Oxford University Press.
35. Dykstra, R. L. (1970). Establishing the positive definiteness of the sample covariance matrix. Annals of Mathematical Statistics, 41(6), 2153–2154.
36. El-Mikkawy, M. E. A. (2004). A fast algorithm for evaluating nth order tridiagonal determinants. Journal of Computational and Applied Mathematics, 166(2), 581–584.
37. Everitt, B. S. (1994a). Exploring multivariate data graphically: A brief review with examples. Journal of Applied Statistics, 21(3), 63–94.
38. Everitt, B. S. (1994b). A Handbook of Statistical Analyses Using S-Plus. London: Chapman and Hall.
39. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and its Applications. London: Chapman and Hall.
40. Feller, W. (1968). An Introduction to Probability Theory and its Applications, Volume I (3rd edition). New York: John Wiley & Sons, Inc.
41. Friedman, J., Hastie, T., and Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432–441.
42. Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley & Sons, Inc.
43. Gabriel, K. R. (1962). Ante-dependence analysis of an ordered set of variables. Annals of Mathematical Statistics, 33(1), 201–212.
44. Greenberg, B. G. and Sarhan, A. E. (1959). Matrix inversion, its interest and application in analysis of data. Journal of the American Statistical Association, 54(288), 755–766.
45. Greenhouse, S. W. and Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95–112.
46. Guttman, L. (1955). A generalized simplex for factor analysis. Psychometrika, 20(3), 173–192.
47. Haggan, V. and Ozaki, T. (1981). Modelling nonlinear random vibration using an amplitude-dependent autoregressive time series model. Biometrika, 68(1), 189–196.
48. Haining, R. (1990). Spatial Data Analysis in the Social and Environmental Sciences. Cambridge: Cambridge University Press.
49. Harville, D. A. (1975). Maximum likelihood approaches to variance component estimation and to related problems. Technical Report No. 75-0175, Aerospace Research Laboratories, Wright-Patterson AFB, Ohio.
50. Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72(358), 320–338.
51. Harville, D. A. (1997). Matrix Algebra from a Statistician’s Perspective. New York: Springer-Verlag.
52. Heagerty, P. J. (2002). Marginalized transition models and likelihood inference for longitudinal categorical data. Biometrics, 58(2), 342–351.
53. Heagerty, P. J. and Zeger, S. L. (2000). Marginalized multilevel models and likelihood inference. Statistical Science, 15(1), 1–19.
54. Hou, W., Garvan, C. W., Zhao, W., Behnke, M., Eyler, F. D., and Wu, R. (2005). A general model for detecting genetic determinants underlying longitudinal traits with unequally spaced measurements and nonstationary covariance structure. Biostatistics, 6(3), 420–433.
55. Huang, J. Z., Liu, L., and Liu, N. (2007). Estimation of large covariance matrices of longitudinal data with basis function approximations. Journal of Computational and Graphical Statistics, 16(1), 189–209.
56. Huang, J. Z., Liu, N., Pourahmadi, M., and Liu, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood. Biometrika, 93(1), 85–98.
57. Huynh, H. and Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1(1), 69–82.
58. Jaffrézic, F. and Pletcher, S. D. (2000). Statistical models for estimating the genetic basis of repeated measures and other function-valued traits. Genetics, 156, 913–922.
59. Jaffrézic, F., Thompson, R., and Hill, W. G. (2003). Structured antedependence models for genetic analysis of repeated measures on multiple quantitative traits. Genetics Research, 82, 55–65.
60. Jaffrézic, F., Thompson, R., and Pletcher, S. D. (2004). Multivariate character process models for the analysis of two or more correlated function-valued traits. Genetics, 168, 477–487.
61. Jaffrézic, F., Venot, E. Laloë, D., Vinet, A., and Renand, G. (2004). Use of structured antedependence models for the genetic analysis of growth curves. Journal of Animal Science, 82, 3465–3473.
62. Jaffrézic, F., White, I. M. S., Thompson, R., and Visscher, P. M. (2002). Contrasting models for lactation curve analysis. Journal of Dairy Science, 85, 968–975.
63. Johnson, K. L. (1989). Higher order antedependence models. Unpublished Ph.D. thesis, Department of Statistics, Pennsylvania State University.
64. Johnson, R. A. and Wichern, D. W. (2002). Applied Multivariate Statistical Analysis, 5th ed. Upper Saddle River, New Jersey: Prentice Hall.
65. Jones, R. H. (1981). Fitting continuous-time autoregressions to discrete data. In D. F. Findley (Ed.), Applied Time Series Analysis II (pp. 651–682). New York: Academic Press.
66. Jones, R. H. (1990). Serial correlation or random subject effects? Communications in Statistics – Simulation and Computation, 19(3), 1105–1123.
67. Jones, R. H. and Ackerson, L. M. (1990). Serial correlation in unequally spaced longitudinal data. Biometrika, 77(4), 721–731.
68. Kearsley, C. G. S., Woolliams, J. A., Coffey, M. P., and Brotherstone, S. (2008). Use of competition data for genetic evaluations of eventing horses in Britain: Analysis of the dressage, showjumping, and cross country phases of eventing competition. Livestock Science, 118, 72–81.
69. Kenward, M. C. (1987). A method for comparing profiles of repeated measurements. Applied Statistics, 36(3), 296–308.
70. Kenward, M. C. (1991). Corrigendum: A method for comparing profiles of repeated measurements. Applied Statistics, 40(2), 379.
71. Krzanowski, W. J. (1993). Antedependence modelling in discriminant analysis of high-dimensional spectroscopic data. In C. M. Cuadras and C. R. Rao (Eds.), Multivariate Analysis: Future Directions 2 (pp. 87–95). Amsterdam: Elsevier.
72. Krzanowski, W. J. (1999). Antedependence models in the analysis of multigroup high-dimensional data. Journal of Applied Statistics, 26(1), 59–67.
73. Krzanowski, W. J., Jonathan, P., McCarthy, W. V., and Thomas, M. R. (1995). Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data. Applied Statistics, 44(1), 101–115.
74. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
75. Lauritzen, S. L. (1996). Graphical Models. Oxford: Clarendon Press.
76. Lee, K. and Daniels, M. J. (2007). A class of Markov models for longitudinal ordinal data. Biometrics, 63(4), 1060–1067.
77. Levina, E., Rothman, A., and Zhu, J. (2008). Sparse estimation of large covariance matrices via a nested lasso penalty. Annals of Applied Statistics, 2(1), 245–263.
78. Lin, M. and Wu, R. (2005). Theoretical basis for the identification of allelic variants that encode drug efficacy and toxicity. Genetics, 170, 919–928.
79. Lin, M. Li, H., Hou, W., Johnson, J. A., and Wu, R. (2007). Modeling sequence-sequence interactions for drug response. Bioinformatics, 23(10), 1251–1257.
80. Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data. Hoboken, New Jersey: John Wiley & Sons, Inc.
81. Macchiavelli, R. E. (1992). Likelihood-based procedures and order selection in higher order antedependence models. Unpublished Ph.D. thesis, Department of Statistics, Pennsylvania State University.
82. Macchiavelli, R. E. and Arnold, S. F. (1994). Variable-order antedependence models. Communications in Statistics – Theory and Methods, 23(9), 2683– 2699.
83. Macchiavelli, R. E. and Arnold, S. F. (1995). Difficulties with the use of penalized likelihood criteria in antedependence and polynomial models. Communications in Statistics – Theory and Methods, 24(2), 501–522.
84. Macchiavelli, R. E. and Moser, E. B. (1997). Analysis of repeated measurements with ante-dependence covariance models. Biometrical Journal, 39(3), 339–350.
85. Mallik, R. K. (2001). The inverse of a tridiagonal matrix. Linear Algebra and its Applications, 325(1), 109–139.
86. Mauchly, J. W. (1940). Significance tests for sphericity of a normal n-variate distribution. Annals of Mathematical Statistics, 11(4), 204–209.
87. Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. New York: Springer.
88. Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4), 308–313.
89. Núñez-Antón, V. and Zimmerman, D. L. (2000). Modeling nonstationary longitudinal data, Biometrics, 56(3), 699–705.
90. Pan, J. and MacKenzie, G. (2003). On modelling mean-covariance structures in longitudinal studies. Biometrika, 90(1), 239–244.
91. Patel, H. I. (1991). Analysis of incomplete data from a clinical trial with repeated measurements. Biometrika, 78(3), 609–619.
92. Pepe, M. and Anderson, G. (1994). A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. Communications in Statistics, Part B – Simulation and Computation, 23(4), 939–951.
93. Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation. Biometrika, 86(3), 677– 690.
94. Pourahmadi, M. (2000). Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix. Biometrika, 87(2), 425– 435.
95. Pourahmadi, M. (2002). Graphical diagnostics for modeling unstructured covariance matrices. International Statistical Review, 70(3), 395–417.
96. Rao, C. R. and Wu, Y. (1989). A strongly consistent procedure for model selection in a regression problem. Biometrika, 76(2), 369–374.
97. Rothman, A. J., Bickel, P. J., Levina, E., and Zhu, J. (2008). Sparse permutation invariant covariance estimation. Electronic Journal of Statistics, 494–515.
98. Roy, S. N. and Sarhan, A. E. (1956). On inverting a class of patterned matrices. Biometrika, 43(1/2), 227–231.
99. Rue, H. and Held, L. (2005). Gaussian Markov Random Fields. Boca Raton, Florida: Chapman & Hall/CRC.
100. Schlegel, P. (1970). The explicit inverse of a tridiagonal matrix. Mathematics of Computation, 24(111), 665.
101. Schott, J. R. (2005). Matrix Analysis for Statistics. Hoboken, New Jersey: John Wiley & Sons, Inc.
102. Smith, M. and Kohn, R. (2002). Parsimonious covariance matrix estimation for longitudinal data. Journal of the American Statistical Association, 97(460), 1141–1153.
103. Sogabe, T. (2008). A fast numerical algorithm for the determinant of a pentadiagonal matrix. Applied Mathematics and Computation, 196(2), 835–841.
104. Tanabe, K. and Sagae, M. (1992). An exact Cholesky decomposition and the generalized inverse of the variance-covariance matrix of the multinomial distribution, with applications. Journal of the Royal Statistical Society, Series B, 54(1), 211–219.
105. Tong, H. (1990). Non-linear Time Series. Oxford: Clarendon Press.
106. Tyler, R. S., Abbas, P., Tye-Murray, N., Gantz, B. J., Knutson, J. F., McCabe, B. F., Lansing, C., Brown, C., Woodworth, G., Hinrichs, J., and Kuk, F. (1988). Evaluation of five different cochlear implant designs: Audiologic assessment and predictors of performance. The Laryngoscope, 98(10), 1100–1106.
107. Verbeke, G., Lesaffre, E., and Brant, L. (1998). The detection of residual serial correlation in linear mixed models. Statistics in Medicine, 17, 1391–1402.
108. Verbeke, G. and Molenberghs, G. (2001). Linear Mixed Models for Longitudinal Data. New York: Springer.
109. Verbyla, A. P. (1993). Modelling variance heterogeneity: Residual maximum likelihood and diagnostics. Journal of the Royal Statistical Society, Series B, 55(2), 493–508.
110. Wall, M. M. (2004). A close look at the spatial structure implied by the CAR and SAR models. Journal of Statistical Planning and Inference, 121, 311– 324.
111. Weiss, R. E. (2005). Modeling Longitudinal Data. New York: Springer.
112. White, J. R. Gardner, L. M., Sees, M., and Corstanje, R. (2008). The shortterm effects of prescribed burning on biomass removal and the release of nitrogen and phosphorus in a treatment wetland. Journal of Environmental Quality, 37, 2386–2391.
113. Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. Chichester: John Wiley & Sons, Inc.
114. Whittle, P. (1954). On stationary processes in the plane. Biometrika, 41(3/4), 434–449.
115. Wong, F., Carter, C. K., and Kohn, R. (2003). Efficient estimation of covariance selection models. Biometrika, 90(4), 809–830.
116. Wu, R. and Hou, W. (2006). A hyperspace model to decipher the genetic architecture of developmental processes: allometry meets ontogeny. Genetics, 172, 627–637.
117. Wu, W. B. and Pourahmadi, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika, 90(4), 831–844.
118. Yuan, M. and Lin, Y. (2007). Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1), 19–35.
119. Zeger, S. L. and Qaqish, B. (1988). Markov regression models for time series: a quasi-likelihood approach. Biometrics, 44(4), 1019–1031.
120. Zhang, P. (2005). Multiple imputation of missing data with ante-dependence covariance structure. Journal of Applied Statistics, 32(2), 141–155.
121. Zhao, W., Chen, Y. Q., Casella, G., Cheverud, J. M., and Wu, R. (2005a). A non-stationary model for functional mapping of complex traits. Bioinformatics, 21(10), 2469–2477.
122. Zhao, W., Hou, W., Littell, R. C., and Wu, R. (2005b). Structured antedependence models for functional mapping of multiple longitudinal traits. Statistical Applications in Genetics and Molecular Biology, 4(1), Article 33.
123. Zimmerman, D. L. (2000). Viewing the correlation structure of longitudinal data through a PRISM. The American Statistician, 54(4), 310–318.
124. Zimmerman, D. L. and Núñez-Antón, V. (1997). Structured antedependence models for longitudinal data. In T.G. Gregoire, D.R. Brillinger, P.J. Diggle, E. Russek-Cohen, W.G. Warren, and R. Wolfinger (Eds.), Modelling Longitudinal and Spatially Correlated Data. Methods, Applications, and Future Directions (pp. 63–76). New York: Springer-Verlag.
125. Zimmerman, D. L. and Núñez-Antón, V. (2001). Parametric modelling of growth curve data: An overview (with Discussion). Test, 10(1), 1–73.
126. Zimmerman, D. L., Núñez-Antón, V., and El-Barmi, H. (1998). Computational aspects of likelihood-based estimation of first-order antedependence models. Journal of Statistical Computation and Simulation, 60, 67–84.